Systems, apparatuses and methods for delivery of ablative energy to tissue

ABSTRACT

A system includes a pulse waveform generator and an ablation device coupled to the pulse waveform generator. The ablation device includes at least one electrode configured for ablation pulse delivery to tissue during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, with a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/416,677, titled “SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OFABLATIVE ENERGY TO TISSUE”, filed May 20, 2019, which is a continuationof U.S. patent application Ser. No. 15/796,375 titled “SYSTEMS,APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”,filed Oct. 27, 2017, now issued as U.S. Pat. No. 10,322,286, which is acontinuation of U.S. patent application Ser. No. 15/334,646 titled“SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TOTISSUE”, filed Oct. 26, 2016, now abandoned, which is a continuation ofPCT Application No. PCT/US2016/057664 titled “SYSTEMS, APPARATUSES ANDMETHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”, filed Oct. 19, 2016,which claims priority to U.S. Provisional Application Ser. No.62/274,926 titled “METHOD AND APPARATUS FOR DELIVERY OF PULSED ELECTRICFIELD ABLATIVE ENERGY TO TISSUE”, filed Jan. 5, 2016, the entiredisclosures of which are incorporated herein by reference in theirentirety.

BACKGROUND

The generation of pulsed electric fields for tissue therapeutics hasmoved from the laboratory to clinical applications over the past twodecades, while the effects of brief pulses of high voltages and largeelectric fields on tissue have been investigated for the past fortyyears or more. Application of brief high DC voltages to tissue, whichcan generate locally high electric fields typically in the range ofhundreds of Volts/centimeter, can disrupt cell membranes by generatingpores in the cell membrane. While the precise mechanism of thiselectrically-driven pore generation or electroporation is unclear, it isthought that the application of relatively large electric fieldsgenerates instabilities in the lipid bilayers in cell membranes, causingthe occurrence of a distribution of local gaps or pores in the membrane.If the applied electric field at the membrane is larger than a thresholdvalue, the electroporation can be irreversible and the pores remainopen, permitting exchange of biomolecular material across the membraneand leading to necrosis and/or apoptosis (cell death). Subsequently thesurrounding tissue heals in a natural process.

Hence, known electroporation applications in medicine and deliverymethods do not address high voltage application, tissue selectivity, andsafe energy delivery, especially in the context of ablation therapy forcardiac arrhythmias with catheter devices. Further, there is an unmetneed for thin, flexible, atraumatic devices that can at the same timeeffectively deliver high DC voltage electroporation ablation therapyselectively to tissue in regions of interest while minimizing damage tohealthy tissue, and for a combination of device design and dosingwaveform that involves minimal or no device repositioning, permitting aneffective, safe and rapid clinical procedure.

SUMMARY

A system includes a pulse waveform generator and an ablation devicecoupled to the pulse waveform generator. The ablation device includes atleast one electrode configured for ablation pulse delivery to tissueduring use. The pulse waveform generator is configured to delivervoltage pulses to the ablation device in the form of a pulsed waveform.A first level of a hierarchy of the pulsed waveform includes a first setof pulses, each pulse having a pulse time duration, with a first timeinterval separating successive pulses. A second level of the hierarchyof the pulsed waveform includes a plurality of first sets of pulses as asecond set of pulses, a second time interval separating successive firstsets of pulses, the second time interval being at least three times theduration of the first time interval.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic illustration of a catheter with a plurality ofelectrodes disposed along its distal shaft, epicardially disposed suchthat it snugly wraps around the pulmonary veins of a cardiac anatomy,according to embodiments.

FIG. 2 is an example waveform showing a sequence of voltage pulses witha pulse width defined for each pulse, according to embodiments.

FIG. 3 schematically illustrates a hierarchy of pulses showing pulsewidths, intervals between pulses, and groupings of pulses, according toembodiments.

FIG. 4 provides a schematic illustration of a nested hierarchy ofmonophasic pulses displaying different levels of nested hierarchy,according to embodiments.

FIG. 5 is a schematic illustration of a nested hierarchy of biphasicpulses displaying different levels of nested hierarchy, according toembodiments.

FIG. 6 schematically shows a circle of numbered catheter electrodes,wherein sets of electrodes can be sequentially selected for applicationof a corresponding sequence of voltage pulse waveforms, according toembodiments.

FIG. 7 illustrates schematically a time sequence of electrocardiogramsand cardiac pacing signals together with atrial and ventricularrefractory time periods and indicating a time window for irreversibleelectroporation ablation, according to embodiments.

FIG. 8 illustrates schematically a time sequence of electrode setactivations delivered as a series of waveform packets over acorresponding series of successive heartbeats, according to embodiments.

FIG. 9 is a schematic illustration of an irreversible electroporationsystem that includes a system console that in turn includes avoltage/signal generator, a controller configured to apply voltages toselected subsets of electrodes and that is communicably connected to acomputer or processor together with a user interface, and a switchingunit configured to electrically isolate other equipment from voltagepulses that may be delivered to an ablation catheter from the voltagegenerator, according to embodiments.

FIG. 10 is a schematic illustration of a user interface in an initialconfiguration, according to embodiments.

FIG. 11 is a schematic illustration of a user interface showing theengagement of an initialization function, according to embodiments.

FIG. 12 is a schematic illustration of a user interface showing arequired step subsequent to initialization, according to embodiments.

FIG. 13 is a schematic illustration of a user interface showing aconfiguration where the system is ready, subsequent to the completion ofa prior step, for delivery of ablative energy. In this configuration theuser interface includes a button for ablation, according to embodiments.

DETAILED DESCRIPTION

The terms “about” and “approximately” as used herein in connection witha referenced numeric indication means the referenced numeric indicationplus or minus up to 10% of that referenced numeric indication. Forexample, the language “about 50” units or “approximately 50” units meansfrom 45 units to 55 units.

In some embodiments, a system includes a pulse waveform generator and anablation device coupled to the pulse waveform generator. The ablationdevice includes at least one electrode configured for ablation pulsedelivery to tissue during use. The pulse waveform generator isconfigured to deliver voltage pulses to the ablation device in the formof a pulsed waveform. A first level of a hierarchy of the pulsedwaveform includes a first set of pulses, each pulse having a pulse timeduration, a first time interval separating successive pulses. A secondlevel of the hierarchy of the pulsed waveform includes a plurality offirst sets of pulses as a second set of pulses, a second time intervalseparating successive first sets of pulses, the second time intervalbeing at least three times the duration of the first time interval. Athird level of the hierarchy of the pulsed waveform includes a pluralityof second sets of pulses as a third set of pulses, a third time intervalseparating successive second sets of pulses, the third time intervalbeing at least 30 times the duration of the second time interval.

In some embodiments, the pulses of each first set of pulses includemonophasic pulses with a voltage amplitude of at least 800 Volts. Insome embodiments, the pulse time duration of each monophasic pulse is inthe range from about 1 microsecond to about 300 microseconds.

In some embodiments, the pulses of each first set of pulses includebiphasic pulses each with a voltage amplitude of at least 800 Volts. Insome embodiments, the pulse time duration of each biphasic pulse is inthe range from about 0.5 nanosecond to about 20 microseconds.

In some embodiments, each second set of pulses includes at least 2 firstsets of pulses and less than 40 first sets of pulses. In someembodiments, each third set of pulses includes at least 2 second sets ofpulses and less than 30 second sets of pulses. In some embodiments, thesecond time interval is at least ten times the pulse time duration.

In some embodiments, the ablation device includes an ablation catheterconfigured for epicardial placement. In some embodiments, the ablationdevice includes an ablation catheter configured for endocardialplacement.

In some embodiments, a system includes a pulse waveform generator, andan ablation device coupled to the pulse waveform generator, the ablationdevice including at least one electrode configured for ablation pulsedelivery to tissue during use. The pulse waveform generator isconfigured to deliver voltage pulses to the ablation device in the formof a pulsed waveform. A first level of a hierarchy of the pulsedwaveform includes a first set of pulses, each pulse having a pulse timeduration, a first time interval separating successive pulses. A secondlevel of the hierarchy of the pulsed waveform includes a plurality offirst sets of pulses as a second set of pulses, a second time intervalseparating successive first set of pulses. In some embodiments, thesecond time interval is at least three times the duration of the firsttime interval. A third level of the hierarchy of the pulsed waveformincludes a plurality of second sets of pulses as a third set of pulses,a third time interval separating successive second sets of pulses. Insome embodiments, the third time interval is at least thirty times theduration of the second time interval. The pulse waveform generator isconfigured to apply a plurality of the third sets of pulses to theablation device with a time delay of at most about 5 millisecondsbetween successive third sets of pulses applied over different electrodesets.

In some embodiments, the ablation device includes an ablation catheterconfigured for epicardial placement. In some embodiments, the ablationcatheter includes at least four electrodes.

In some embodiments, each second set of pulses includes at least 2 firstsets of pulses and less than 40 first sets of pulses. In someembodiments, each third set of pulses includes at least 2 second sets ofpulses and less than 30 second sets of pulses. In some embodiments, thepulses of each first set of pulses has a voltage amplitude of at least800 Volts.

In some embodiments, a system includes a pulse waveform generator and anablation device coupled to the pulse waveform generator, the ablationdevice including at least one electrode configured for ablation pulsedelivery to tissue during use. The system also includes a cardiacstimulator coupled to the pulse waveform generator, the cardiacstimulator configured for generating pacing signals for cardiacstimulation during use. The pulse waveform generator is configured todeliver voltage pulses to the ablation device in the form of a pulsedwaveform, the pulsed waveform being in synchrony with the pacingsignals. A first level of a hierarchy of the pulsed waveform includes afirst set of pulses, each pulse having a pulse time duration, a firsttime interval separating successive pulses. A second level of thehierarchy of the pulsed waveform includes a plurality of first sets ofpulses as a second set of pulses, a second time interval separatingsuccessive first sets of pulses. A third level of the hierarchy of thepulsed waveform includes a plurality of second sets of pulses as a thirdset of pulses, a third time interval separating successive second setsof pulses. The pulse waveform generator is configured to generate thepulsed waveform such that each of the first sets of pulses and each ofthe second sets of pulses, the plurality of second sets of pulses, thepredetermined number of electrode sets, the time delay, the pulse timeduration, the first time interval, the second time interval, and thethird time interval are jointly constrained by a Diophantine inequality.

In some embodiments, the Diophantine inequality constraint is furthercharacterized by a refractory time window. In some embodiments, a numberof the first sets of pulses and a number of the second sets of pulsesare pre-determined.

In some embodiments, the pulse waveform generator is further configuredto deliver the pulsed waveform spaced from the pacing signals by a timeoffset, the time offset being smaller than about 25 milliseconds. Insome embodiments, the third time interval corresponds to a pacing periodassociated with the pacing signals. In some embodiments, the second timeinterval is at least three times the duration of the first timeinterval. In some embodiments, the third time interval is at leastthirty times the duration of the second time interval. In someembodiments, the second level time interval is at least ten times theduration of the pulse time duration.

In some embodiments, the ablation device includes an ablation catheterconfigured for epicardial placement. In some embodiments, the ablationdevice includes an ablation catheter configured for endocardialplacement.

In some embodiments, a system includes a pulse waveform generatorincluding a user interface and an ablation device coupled to the pulsewaveform generator, the ablation device including a plurality ofelectrodes configured for ablation pulse delivery to tissue of a patientduring use. The system also includes a cardiac stimulator coupled to thepulse waveform generator, the cardiac stimulator configured forgenerating pacing signals for cardiac stimulation of the patient duringuse. The pulse waveform generator is configured to deliver voltagepulses to the ablation device in the form of a pulsed voltage waveformhaving at least three levels of hierarchy. The pulse waveform generatoris further configured to deliver the pulsed voltage waveform insynchrony with the pacing signals, and to deliver the pulsed voltagewaveform upon receipt of the indication of user confirmation.

In some embodiments, a first level of a hierarchy of the pulsed waveformincludes a first set of pulses, each pulse having a pulse time duration,a first time interval separating successive pulses. In some embodiments,a second level of the hierarchy of the pulsed waveform includes aplurality of first sets of pulses as a second set of pulses, a secondtime interval separating successive first sets of pulses. In someembodiments, a third level of the hierarchy of the pulsed waveformincludes a plurality of second sets of pulses as a third set of pulses,a third time interval separating successive second sets of pulses. Insome embodiments, the pulse waveform generator is further configured toapply a plurality of third sets of pulses to a predetermined number ofelectrode sets of the ablation device with a time delay betweensuccessive third sets of pulses. In some embodiments, each of the firstsets of pulses and each of the second sets of pulses, the predeterminednumber of electrode sets, the time delay, the pulse time duration, thefirst time interval, the second time interval, and the third timeinterval are jointly constrained by a Diophantine inequality.

In some embodiments, the pulse waveform generator is configured todeliver the pulsed waveform only after a pre-determined time intervalafter the indication of user confirmation. In some embodiments, the userinterface includes a control input device, and the pulse waveformgenerator is configured to deliver the pulsed waveform upon userengagement of the control input device.

In some embodiments, a method includes generating a pulsed waveform. Thepulsed waveform includes a first level of a hierarchy of the pulsedwaveform that includes a first set of pulses, each pulse having a pulsetime duration, a first time interval separating successive pulses. Thepulse waveform also includes a second level of the hierarchy of thepulsed waveform that includes a plurality of first sets of pulses as asecond set of pulses, a second time interval separating successive firstsets of pulses, the second time interval being at least three times theduration of the first time interval. The pulse waveform a third level ofthe hierarchy of the pulsed waveform includes a plurality of second setsof pulses as a third set of pulses, a third time interval separatingsuccessive second sets of pulses, the third time interval being at leastthirty times the duration of the second level time interval. The methodalso includes delivering the pulsed waveform to an ablation device.

In some embodiments, a method includes generating a pulsed waveform. Thepulsed waveform includes a first level of a hierarchy of the pulsedwaveform that includes a first set of pulses, each pulse having a pulsetime duration, a first time interval separating successive pulses. Thepulsed waveform also includes a second level of the hierarchy of thepulsed waveform that includes a plurality of first sets of pulses as asecond set of pulses, a second time interval separating successive firstsets of pulses, the second time interval being at least three times theduration of the first time interval. The pulsed waveform also includes athird level of the hierarchy of the pulsed waveform includes a pluralityof second sets of pulses as a third set of pulses, a third time intervalseparating successive second sets of pulses, the third time intervalbeing at least thirty times the duration of the second level timeinterval. The method also includes generating pacing signals with acardiac stimulator. The method also includes delivering, in synchronywith the pacing signals, the pulsed waveform to an ablation device.

Disclosed herein are methods, systems and apparatuses for the selectiveand rapid application of pulsed electric fields/waveforms to effecttissue ablation with irreversible electroporation. Some embodiments aredirected to pulsed high voltage waveforms together with a sequenceddelivery scheme for delivering energy to tissue via sets of electrodes.In some embodiments, the electrodes are catheter-based electrodes, or aplurality of electrodes disposed along the length of an elongate medicaldevice. In some embodiments, a system useful for irreversibleelectroporation includes a voltage/signal generator and a controllercapable of being configured to apply pulsed voltage waveforms to aselected plurality or a subset of electrodes of an ablation device. Insome embodiments, the controller is configured to control inputs wherebyselected pairs of anode-cathode subsets of electrodes can besequentially triggered based on a pre-determined sequence, and in oneembodiment the sequenced delivery can be triggered from a cardiacstimulator or pacing system/device. In some embodiments, the ablationpulse waveforms are applied in a refractory period of the cardiac cycleso as to avoid disruption in rhythm regularity of the heart. One examplemethod of enforcing this is to electrically pace the heart with acardiac stimulator and ensure pacing capture to establish periodicityand predictability of the cardiac cycle, and then to define a timewindow well within the refractory period of this periodic cycle withinwhich the ablation waveform is delivered.

In some embodiments, the pulsed voltage waveforms disclosed herein arehierarchical in organization and have a nested structure. In someembodiments, the pulsed waveform includes hierarchical groupings ofpulses with a variety of associated timescales. Furthermore, theassociated timescales and pulse widths, and the numbers of pulses andhierarchical groupings, can be selected so as to satisfy one or more ofa set of Diophantine inequalities involving the frequency of cardiacpacing.

Pulsed waveforms for electroporation energy delivery as disclosed hereincan enhance the safety, efficiency and effectiveness of the energydelivery by reducing the electric field threshold associated withirreversible electroporation, yielding more effective ablative lesionswith reduced total energy delivered. This in turn can broaden the areasof clinical application of electroporation including therapeutictreatment of a variety of cardiac arrhythmias.

The present disclosure addresses the need for devices and methods forrapid, selective and safe delivery of irreversible electroporationtherapy, generally with multiple devices, such that, in someembodiments, peak electric field values can be reduced and/or minimizedwhile at the same time sufficiently large electric field magnitudes canbe maintained in regions where tissue ablation is desired. This alsoreduces the likelihood of excessive tissue damage or the generation ofelectrical arcing, and locally high temperature increases.

FIG. 1 is a schematic illustration of a catheter 15 with a plurality ofelectrodes disposed along its shaft. The catheter is shown in FIG. 1 inrelation to a heart 7 and the catheter 15 is wrapped epicardially aroundthe pulmonary veins of the left atrium denoted by reference characters10, 11, 12 and 13 (respectively Left Superior, Left Inferior, RightSuperior and Right Inferior in FIG. 1) and has electrodes indicated bydark bands (such as those denoted by reference character 17 in FIG. 1)that are wrapped and/or looped in a contour around the pulmonary veins10, 11, 12, 13 of the left atrium. In some embodiment, catheter ends 8and 9 are tightly drawn together and held inside a cinching tool (notshown) in order to ensure that the catheter electrodes are snuglywrapped around the pulmonary veins 10, 11, 12, 13. A method andapparatus using a subxiphoid pericardial access location and aguidewire-based delivery method to accomplish the placement of amulti-electrode ablation catheter around the pulmonary veins wasdescribed in PCT Patent Application Publication No. WO2014/025394,entitled “Catheters, Catheter Systems and Methods for Puncturing Througha Tissue Structure and Ablating a Tissue Region”, the entire disclosureof which are incorporated herein by reference in its entirety.

In some embodiments, the catheter electrodes 17 can be constructed inthe form of metallic bands or rings. In some embodiments, each electrode17 can be constructed so as to be flexible. For example, the electrodes17 can be in the form of metallic coiled springs or helical windingsaround the shaft of the catheter 15. As another example, theelectrode(s) 17 can be in the form of a series of metallic bands orrings disposed along the shaft and that are electrically connectedtogether, with the flexible portions of catheter shaft between theelectrodes providing flexibility to the entire electrode. In someembodiments, at least a portion of the electrodes 17 can includebiocompatible metals such as, but not limited to, titanium, palladium,silver, platinum and/or platinum alloys. In some embodiments, at least aportion of the electrodes 17 includes platinum and/or platinum alloys.In some embodiments, the catheter shaft can be made of a flexiblepolymeric material such as (for purposes of non-limiting examples only)polytetrafluorethylene, polyamides such as nylon, or polyether blockamide. The electrodes 17 can be connected to insulated electrical leads(not shown) leading to a proximal handle portion of the catheter 15 (notshown), with the insulation on each of the leads being capable ofsustaining an electrical potential difference of at least 700V acrossits thickness without dielectric breakdown. While the catheter 15 isplaced epicardially as shown in FIG. 1, i.e. beneath the pericardium, inalternate embodiments the ablation catheter can be additionally oralternatively useful for endocardial placement.

FIG. 2 illustrates a pulsed voltage waveform in the form of a sequenceof rectangular double pulses, with each pulse, such as the pulse 101being associated with a pulse width or duration. The pulsewidth/duration can be about 0.5 microseconds, about 1 microsecond, about5 microseconds, about 10 microseconds, about 25 microseconds, about 50microseconds, about 100 microseconds, about 125 microseconds, about 140microseconds, about 150 microseconds, including all values andsub-ranges in between. The pulsed waveform of FIG. 2 illustrates a setof monophasic pulses where the polarities of all the pulses are the same(all positive in FIG. 2, as measured from a zero baseline). In someembodiments, such as for irreversible electroporation applications, theheight of each pulse 101 or the voltage amplitude of the pulse 101 canbe about 400 Volts, about 1000 Volts, about 5000 Volts, about 10,000Volts, about 15,000 Volts, including all values and sub ranges inbetween. As illustrated in FIG. 2, the pulse 101 is separated from aneighboring pulse by a time interval 102, also sometimes referred to asa first time interval. The first time interval can be about 10microseconds, about 50 microsecond, about 100 microseconds, about 200microseconds, about 500 microseconds, about 800 microseconds, about 1millisecond including all values and sub ranges in between, in order togenerate irreversible electroporation.

FIG. 3 introduces a pulse waveform with the structure of a hierarchy ofnested pulses. FIG. 3 shows a series of monophasic pulses such as pulse115 with pulse width/pulse time duration w, separated by a time interval(also sometimes referred to as a first time interval) such as 118 ofduration t₁ between successive pulses, a number m₁ of which are arrangedto form a group of pulses 121 (also sometimes referred to as a first setof pulses). Furthermore, the waveform has a number m₂ of such groups ofpulses (also sometimes referred to as a second set of pulses) separatedby a time interval 119 (also sometimes referred to as a second timeinterval) of duration t₂ between successive groups. The collection of m₂such pulse groups, marked by 122 in FIG. 3, constitutes the next levelof the hierarchy, which can be referred to as a packet and/or as asecond set of pulses. The pulse width and the time interval t₁ betweenpulses can both be in the range of microseconds to hundreds ofmicroseconds, including all values and sub ranges in between. In someembodiments, the time interval t₂ can be at least three times largerthan the time interval t₁. In some embodiments, the ratio t₂/t₁ can bein the range between about 3 and about 300, including all values andsub-ranges in between.

FIG. 4 further elaborates the structure of a nested pulse hierarchywaveform. In this figure, a series of m₁ pulses (individual pulses notshown) form a group of pulses 130 (e.g., a first set of pulses). Aseries of m₂ such groups separated by an inter-group time interval 142of duration t₂ (e.g., a second time interval) between one group and thenext form a packet 132 (e.g., a second set of pulses). A series of m₃such packets separated by time intervals 144 of duration t₃ (e.g., athird time interval) between one packet and the next form the next levelin the hierarchy, a super-packet labeled 134 (e.g., a third set ofpulses) in the figure. In some embodiments, the time interval t₃ can beat least about thirty times larger than the time interval t₂. In someembodiments, the time interval t₃ can be at least fifty times largerthan the time interval t₂. In some embodiments, the ratio t₃/t₂ can bein the range between about 30 and about 800, including all values andsub-ranges in between. The amplitude of the individual voltage pulses inthe pulse hierarchy can be anywhere in the range from 500 Volts to 7,000Volts or higher, including all values and sub ranges in between.

FIG. 5 provides an example of a biphasic waveform sequence with ahierarchical structure. In the example shown in the figure, biphasicpulses such as 151 have a positive voltage portion as well as a negativevoltage portion to complete one cycle of the pulse. There is a timedelay 152 (e.g., a first time interval) between adjacent cycles ofduration t₁, and n₁ such cycles form a group of pulses 153 (e.g., afirst set of pulses). A series of n₂ such groups separated by aninter-group time interval 156 (e.g., a second time interval) of durationt₂ between one group and the next form a packet 158 (e.g., a second setof pulses). The figure also shows a second packet 162, with a time delay160 (e.g., a third time interval) of duration t₃ between the packets.Just as for monophasic pulses, higher levels of the hierarchicalstructure can be formed as well. The amplitude of each pulse or thevoltage amplitude of the biphasic pulse can be anywhere in the rangefrom 500 Volts to 7,000 Volts or higher, including all values and subranges in between. The pulse width/pulse time duration can be in therange from nanoseconds or even sub-nanoseconds to tens of microseconds,while the delays t₁ can be in the range from zero to severalmicroseconds. The inter-group time interval t₂ can be at least ten timeslarger than the pulse width. In some embodiments, the time interval t₃can be at least about twenty times larger than the time interval t₂. Insome embodiments, the time interval t₃ can be at least fifty timeslarger than the time interval t₂.

Embodiments disclosed herein include waveforms structured ashierarchical waveforms that include waveform elements/pulses at variouslevels of the hierarchy. The individual pulses such as 115 in FIG. 3comprise the first level of the hierarchy, and have an associated pulsetime duration and a first time interval between successive pulses. A setof pulses, or elements of the first level structure, form a second levelof the hierarchy such as the group of pulses/second set of pulses 121 inFIG. 3. Among other parameters, associated with the waveform areparameters such as a total time duration of the second set of pulses(not shown), a total number of first level elements/first set of pulses,and second time intervals between successive first level elements thatdescribe the second level structure/second set of pulses. In someembodiments, the total time duration of the second set of pulses can bebetween about 20 microseconds and about 10 milliseconds, including allvalues and sub-ranges in between. A set of groups, second set of pulses,or elements of the second level structure, form a third level of thehierarchy such as the packet of groups/third set of pulses 122 in FIG.3. Among other parameters, there is a total time duration of the thirdset of pulses (not shown), a total number of second levelelements/second set of pulses, and third time intervals betweensuccessive second level elements that describe the third levelstructure/third set of pulses. In some embodiments, the total timeduration of the third set of pulses can be between about 60 microsecondsand about 200 milliseconds, including all values and sub ranges inbetween. The generally iterative or nested structure of the waveformscan continue to a higher plurality of levels, such as ten levels ofstructure, or more.

In some embodiments, hierarchical waveforms with a nested structure andhierarchy of time intervals as described herein are useful forirreversible electroporation ablation energy delivery, providing a gooddegree of control and selectivity for applications in different tissuetypes. A variety of hierarchical waveforms can be generated with asuitable pulse generator. It is understood that while the examplesherein identify separate monophasic and biphasic waveforms for clarity,it should be noted that combination waveforms, where some portions ofthe waveform hierarchy are monophasic while other portions are biphasic,can also be generated/implemented.

In embodiments directed to treatment of cardiac ablation, the pulsewaveforms described above can be applied with electrode bipoles selectedfrom a set of electrodes on a catheter, such as an ablation catheter. Asubset of electrodes of the catheter can be chosen as anodes, whileanother subset of electrodes of the ablation catheter can be chosen ascathodes, with the voltage waveform being applied between anodes andcathodes. As a non-limiting example, in instances where the ablationcatheter is an epicardially placed ablation catheter, the catheter canbe wrapped around the pulmonary veins, and one electrode can be chosenas anode and another electrode can be chosen as cathode. FIG. 6illustrates an example circular catheter configuration, whereapproximately diametrically opposite electrode pairs (e.g., electrodes603 and 609, electrodes 604 and 610, electrodes 605 and 611, andelectrodes 606 and 612) are activatable as anode-cathode sets. Any ofthe pulse waveforms disclosed can be progressively or sequentiallyapplied over a sequence of such electrode sets. As a non-limitingexample, FIG. 6 depicts a sequence of electrode subset activations. As afirst step, electrodes 603 and 609 are selected as anode and cathoderespectively, and a voltage waveform with a hierarchical structuredescribed herein is applied across these electrodes. With a small timedelay (e.g., less than about 5 milliseconds), as a next step electrodes604 and 610 are selected as anode and cathode respectively, and thewaveform is applied again across this set of electrodes. After a smalltime delay, as a next step electrodes 605 and 611 are selected as anodeand cathode respectively for the next application of the voltagewaveform. In the next step, after a small time delay, electrodes 606 and612 are selected as anode and cathode respectively for voltage waveformapplication. In some embodiments, one or more of the waveforms appliedacross electrode pairs is applied during the refractory period of acardiac cycle, as described in more detail herein.

In some embodiments, the ablation pulse waveforms described herein areapplied during the refractory period of the cardiac cycle so as to avoiddisruption of the sinus rhythm of the heart. In some embodiments, amethod of treatment includes electrically pacing the heart with acardiac stimulator to ensure pacing capture to establish periodicity andpredictability of the cardiac cycle, and then defining a time windowwithin the refractory period of the cardiac cycle within which one ormore pulsed ablation waveforms can be delivered. FIG. 7 illustrates anexample where both atrial and ventricular pacing is applied (forinstance, with pacing leads or catheters situated in the right atriumand right ventricle respectively). With time represented on thehorizontal axis, FIG. 7 illustrates a series of ventricular pacingsignals such as 64 and 65, and a series of atrial pacing signals such as62 and 63, along with a series of ECG waveforms 60 and 61 that aredriven by the pacing signals. As indicated in FIG. 7 by the thickarrows, there is an atrial refractory time window 68 and a ventricularrefractory time window 69 that respectively follow the atrial pacingsignal 62 and the ventricular pacing signal 64. As shown in FIG. 7, acommon refractory time window 66 of duration T_(r) can be defined thatlies within both atrial and ventricular refractory time windows 68, 69.In some embodiments, the electroporation ablation waveform(s) can beapplied in this common refractory time window 66. The start of thisrefractory time window 68 is offset from the pacing signal 64 by a timeoffset 59 as indicated in FIG. 7. The time offset 59 can be smaller thanabout 25 milliseconds, in some embodiments. At the next heartbeat, asimilarly defined common refractory time window 67 is the next timewindow available for application of the ablation waveform(s). In thismanner, the ablation waveform(s) may be applied over a series ofheartbeats, at each heartbeat remaining within the common refractorytime window. In one embodiment, each packet of pulses as defined abovein the pulse waveform hierarchy can be applied over a heartbeat, so thata series of packets is applied over a series of heartbeats, for a givenelectrode set.

A timing sequence of electrode activation over a series of electrodesets is illustrated in FIG. 8, according to embodiments. Using theexample scenario where it is desired to apply a hierarchical ablationwaveform to j electrode sets (each electrode set comprising in generalat least one anode and at least one cathode, in some embodiments,cardiac pacing is utilized as described in the foregoing, and a packetof pulses (such as including one or more pulse groups, or one or moresets of pulses) is applied first to electrode set 1, and with only asmall time delay t_(d) (of the order of about 100 μs or less) this isfollowed by the packet of pulses being applied to electrode set 2.Subsequently, with another time delay, the packet of pulses is appliedto electrode set 3, and so on to electrode set j. This sequence 632 ofapplications of the packet of pulses to all the j electrode sets isdelivered during a single heartbeat's refractory time window (such asthe common refractory time window 66 or 67), and each application to anelectrode set constitutes one packet for that electrode set. Considernow the case of a monophasic hierarchical waveform. Referring to themonophasic waveform example shown in FIG. 3, the waveform has a seriesof monophasic pulses each with pulse width w, separated by a timeinterval of duration t₁ between successive pulses, a number m₁ of whichare arranged to form a group of pulses. Furthermore, the waveform has anumber m₂ of such groups of pulses separated by a time interval ofduration t₂ between successive groups, thereby defining a packet. Ifthis waveform is applied in sequence over the j electrode sets asdescribed here, we can write the inequality

j[m ₂(m ₁ w+t ₁(m ₁−1))+t ₂(m ₂−1)]+t _(d)(j−1)<T _(r)  (1)

that the pulse waveform parameters m₁ and m₂ must satisfy for a givennumber of electrode sets j, in order for the entire ablation pulsedelivery to occur within a refractory time window T_(r). In someembodiments, the refractory time window T_(r) can be about 140milliseconds or less. The time offset of the start of the refractorywindow with respect to a pacing signal can be less than about 10milliseconds. While the time intervals w, t₁, t₂ and t_(d) can bearbitrary, when implemented with finite state machines such as (forexample) a computer processor, they are integers as measured in somesuitable units (such as, for example, microseconds, nanoseconds ormultiples of a fundamental processor clock time period). Given a numberof electrode sets j, equation (1) represents a Diophantine inequalitymutually constraining the pulse waveform parameters (pulse width, timeintervals and numbers of pulses and groups) such that the total durationof the waveform application over the j electrode sets is smaller than agiven common refractory period. In some embodiments, a solution set forthe Diophantine inequality can be found based on partial constraints onthe pulse waveform parameters. For example, the generator can requireinput of some of the pulse waveform parameters and/or relatedparameters, for example the pulse width w and time delay t_(d), afterwhich the system console determines the rest of the pulse waveformparameters. In this case the number of electrode sets j is also an inputto the system that constrains the solution determination. In oneembodiment the system console could display more than one such possiblesolution set of waveform parameters for the user to make a selection,while in an alternate embodiment the system makes an automatic selectionor determination of the waveform parameters. In some embodiments, asolution can be calculated and directly implemented in pre-determinedform, such as, for example, on a pulse generator system console. Forexample, all of the pulse waveform parameters are pre-determined tosatisfy a Diophantine inequality similar to equation (1) and thewaveform is pre-programmed on the system; possibly the pre-determinedsolution(s) can depend on the number of electrode sets j, or alternatelythe solution(s) can be pre-determined assuming a maximal number for theelectrode sets. In some embodiments more than one solution could bepre-determined and made available for user selection on the systemconsole.

While the Diophantine inequality (1) holds for delivery of a singlewaveform packet over a single refractory time window, the full waveformcan sometimes involve a plurality of packets. The number of packets canbe pre-determined and in one embodiment can range from 1 to 28 packets,including all values and sub ranges in between. The appropriaterefractory time window T_(r) can be pre-determined and/or pre-defined inone embodiment or, in an alternate embodiment, it can be selected by auser from within a certain pre-determined range. While inequality (1)was explicitly written for a monophasic hierarchical waveform, a similarinequality may be written for a biphasic waveform, or for a waveformthat combines monophasic and biphasic elements.

A schematic illustration of ablation waveform delivery over multipleelectrode sets j with a series of packets at the top level of thewaveform hierarchy is provided in FIG. 8. The first waveform packet 632is delivered over a sequence of j electrode sets in succession over theentire electrode sequence; the waveform parameters for this sequencesatisfy a Diophantine inequality such as equation (1). This entirevoltage waveform sequence is delivered within a defined refractory timewindow of a single paced heartbeat. After a packet delay t₃ equal to onepacing period, the next waveform packet 633 is delivered over the jelectrode sets in succession over the entire electrode sequence with thesame waveform parameters. The waveform delivery is continued over thepre-determined number of packets until the last waveform packet 636 isdelivered over the j electrode sets in succession. Thus ablationdelivery occurs over as many paced heartbeats as there are packets. Thevoltage amplitude for the waveform can range between approximately 700Vand approximately 10,000V, and more preferably between approximately1,000V and approximately 8,000V, as suitable and convenient for theclinical application, including all values and sub ranges in between.

In some embodiments, the complete sequence of electrode sets can besubdivided into smaller subsequences of electrode sets/electrodesubsets. For example, the complete sequence of j electrode sets can besubdivided into N subsequences with j₁ electrode sets in the firstsubsequence/first subset, j₂ electrode sets in the secondsubsequence/second subset, and so on, with j_(N) electrode sets in theN-th subsequence. The waveform packets are applied first over the firstsubsequence of j₁ electrode sets, then over the second subsequence of j₂electrode sets, and so on, with cardiac pacing employed throughout andall waveform packets applied within appropriate refractory time windows.

FIG. 9 is a schematic illustration of a system architecture for anablation system 200 configured for delivery of pulsed voltage waveforms.The system 200 includes a system console 215, which in turn includes apulsed waveform generator and controller 202, a user interface 203, anda switch 205 for isolating a connection box 210 (to which multiplecatheters may be connected) from voltage pulses delivered by thegenerator. In some embodiments, the generator/controller 202 can includea processor, which can be any suitable processing device configured torun and/or execute a set of instructions or code. The processor can be,for example, a general purpose processor, a Field Programmable GateArray (FPGA), an Application Specific Integrated Circuit (ASIC), aDigital Signal Processor (DSP), and/or the like. The processor can beconfigured to run and/or execute application processes and/or othermodules, processes and/or functions associated with the system and/or anetwork associated therewith (not shown).

In some embodiments, the system 200 can also include a memory and/or adatabase (not shown) configured for, for example, storing pacing data,waveform information, and/or the like. The memory and/or the databasecan independently be, for example, a random access memory (RAM), amemory buffer, a hard drive, a database, an erasable programmableread-only memory (EPROM), an electrically erasable read-only memory(EEPROM), a read-only memory (ROM), Flash memory, and/or so forth. Thememory and/or the database can store instructions to cause thegenerator/controller 202 to execute modules, processes and/or functionsassociated with the system 200, such as pulsed waveform generationand/or cardiac pacing.

The system 200 can be in communication with other devices (not shown)via, for example, one or more networks, each of which can be any type ofnetwork such as, for example, a local area network (LAN), a wide areanetwork (WAN), a virtual network, a telecommunications network, and/orthe Internet, implemented as a wired network and/or a wireless network.Any or all communications can be secured (e.g., encrypted) or unsecured,as is known in the art. The system 200 can include and/or encompass apersonal computer, a server, a work station, a tablet, a mobile device,a cloud computing environment, an application or a module running on anyof these platforms, and/or the like.

The system console 215 delivers ablation pulses to an ablation catheter209 that is suitably positioned in a patient anatomy such as, forexample, in a loop around the patient's pulmonary veins in a pericardialspace of the patient's heart. An intracardiac ECG recording and pacingcatheter 212 is coupled to an ECG recording system 208 via theconnection box 210. The ECG recording system 208 is connected to acardiac stimulator or pacing unit 207. The cardiac stimulator 207 cansend a pacing output to the recording and pacing catheter 212; ingeneral both atrial and ventricular pacing signals can be generated asoutputs from the cardiac stimulator 207, and in some embodiments therecan be separate intracardiac atrial and ventricular pacing catheters(not shown) or leads, each of which can then be disposed and/orpositioned in the appropriate cardiac chamber. The same pacing outputsignal is also sent to the ablation system console 215. The pacingsignal is received by the ablation system console and, based on thepacing signal, the ablation waveform can be generated by thegenerator/controller 202 within a common refractory window as describedherein. In some embodiments, the common refractory window can startsubstantially immediately following the ventricular pacing signal (orafter a very small delay) and last for a duration of approximately 130ms or less thereafter. In this case, the entire ablation waveform packetis delivered within this duration, as explained earlier.

The user interface 203 associated with the ablation system console 215can be implemented in a variety of forms as convenient for theapplication. When an epicardial ablation catheter is delivered via asubxiphoid approach and is placed epicardially around the pulmonaryveins as shown in FIG. 1, it may be cinched in place at the ends 8 and 9by passing the ends through a cinch tool. Depending on the size of thespecific left atrial anatomy, a subset of the electrodes may be disposedaround the pulmonary veins in encircling fashion while a remainder ofthe electrodes may be pulled inside the cinch tool (not shown in FIG. 1)and thus are not exposed. In such embodiments, the encircling/exposedelectrodes can be selectively used for delivering ablation energy. Anembodiment of a user interface suitable for use with an ablationcatheter is schematically depicted in FIG. 10. In FIG. 10, a userselects the number of proximal electrodes inside the cinch tool and thenumber of distal electrodes inside the cinch tool as indicated inwindows 653 and 654 respectively where the user has made selections 650and 651 respectively for the respective numbers of electrodes. Thecomplementary electrodes/subset of electrodes on the catheter (takenfrom the full set of catheter electrodes) that are not inside the cinchtool are the exposed electrodes to be used in the delivery of pulsedelectric fields for electroporation ablation. The amplitude of thewaveform to be delivered is controlled by an input mechanism such as,for example, the slider 658 that can be moved over a pre-determinedvoltage range indicated by 657 in FIG. 10. Once a voltage amplitude hasbeen selected, an initialization (or Initialize) button 655 provided onthe user interface is engaged to ready the ablation system for energydelivery. In one example, this can take the form of a trigger forcharging a capacitor bank to store energy for subsequent delivery to thecatheter.

As shown in FIG. 11, the Initialize button 660 can also act as a statusindicator that indicates that the initialization process is ongoing. Thestatus can be indicated by text (“Initializing . . . ” as shown in FIG.11, and/or color, such as yellow to indicate that initialization has notyet started or is still in progress). Once the initialization process iscomplete (e.g., a capacitor bank is fully or satisfactorily charged), asshown in FIG. 12, the same button 663 now indicates completion of theprocess (“Initialized”) and, in some embodiments as illustrated, it canchange color (e.g. change from yellow to green) and/or shape to furtherindicate completion of initialization. Meanwhile, the ablation systemawaits reception of a pacing signal from a cardiac stimulator or pacingunit. Once a pacing signal is detected and/or confirmed together withcompletion of the initialization process, a second button 665 nowbecomes available for a user to engage, for confirmation of pacingcapture. If a pacing signal is not detected by the ablation systemconsole, then the second button 665 is not enabled. The user can monitoran ECG display (not shown) to view the cardiac stimulator pacing outputin conjunction with intracardiac ECG recordings in order to confirmpacing capture (this confirms that atrial and ventricular contractionsare indeed driven by the pacing signal, in order to establish apredictable common refractory window). Once the user visually confirmspacing capture from the ECG data, (s)he can then engage the “ConfirmPacing Capture” button 665 to confirm pacing capture on the ablationsystem.

As shown in FIG. 13, once pacing capture is confirmed on the ablationsystem, the system is now available for ablation or pulsed electricfield delivery. The pacing capture confirmation button now changesappearance 670 (the appearance can change in color, shape, and/or thelike) and indicates readiness for ablation delivery as shown by 670.Furthermore, an ablation delivery button 675 now becomes available tothe user. The user can engage the ablation delivery button 675 todeliver ablation in synchrony with the paced heart rhythm. In someembodiments, the user engages the button 675 for the duration ofablation delivery, at the end of which the button changes shape or colorto indicate completion of ablation delivery. In some embodiments, if theuser disengages from the button 675 before ablation delivery iscompleted, ablation delivery is immediately stopped with only a smalltime lag of no more than, for example, 20 ms. In some embodiments, ifthe user has not engaged the ablation button 675 after it is displayedas being available, it stays available for engagement for only a limitedtime duration before it is disabled, as a safety mechanism. In someembodiments the ablation button 675 can be a software or graphic buttonon a user interface display, while in another embodiment it could be amechanical button whose response depends on its state of activation oravailability as determined by the system, or in another embodiment, thebutton 675 can be without limitation in the form of any of a variety ofcontrol input devices such as a lever, joystick, computer mouse, and soon. In one embodiment, the ablation system can have a separateemergency-stop button for additional safety, for example if it isdesired to instantly de-activate the system. In one embodiment, theablation console can be mounted on a rolling trolley or wheeled cart,and the user can control the system using a touchscreen interface thatis in the sterile field. The touchscreen can be for example an LCDtouchscreen in a plastic housing mountable to a standard medical rail orpost and the touchscreen can have at a minimum the functionalitydescribed in the foregoing. The interface can for example be coveredwith a clear sterile plastic drape.

The waveform parameters as detailed herein can be determined by thedesign of the signal generator, and in some embodiments the parameterscan be pre-determined. In some embodiments, at least a subset of thewaveform parameters could be determined by user control as may beconvenient for a given clinical application. The specific examples anddescriptions herein are exemplary in nature and variations can bedeveloped by those skilled in the art based on the material taughtherein without departing from the scope of embodiments disclosed herein.

One or more embodiments described herein relate to a computer storageproduct with a non-transitory computer-readable medium (also can bereferred to as a non-transitory processor-readable medium) havinginstructions or computer code thereon for performing variouscomputer-implemented operations. The computer-readable medium (orprocessor-readable medium) is non-transitory in the sense that it doesnot include transitory propagating signals per se (e.g., a propagatingelectromagnetic wave carrying information on a transmission medium suchas space or a cable). The media and computer code (also can be referredto as code or algorithm) may be those designed and constructed for thespecific purpose or purposes. Examples of non-transitorycomputer-readable media include, but are not limited to, magneticstorage media such as hard disks, floppy disks, and magnetic tape;optical storage media such as Compact Disc/Digital Video Discs(CD/DVDs), Compact Disc-Read Only Memories (CD-ROMs), and holographicdevices; magneto-optical storage media such as optical disks; carrierwave signal processing modules; and hardware devices that are speciallyconfigured to store and execute program code, such asApplication-Specific Integrated Circuits (ASICs), Programmable LogicDevices (PLDs), Read-Only Memory (ROM) and Random-Access Memory (RAM)devices. Other embodiments described herein relate to a computer programproduct, which can include, for example, the instructions and/orcomputer code disclosed herein.

One or more embodiments and/or methods described herein can be performedby software (executed on hardware), hardware, or a combination thereof.Hardware modules may include, for example, a general-purpose processor(or microprocessor or microcontroller), a field programmable gate array(FPGA), and/or an application specific integrated circuit (ASIC).Software modules (executed on hardware) can be expressed in a variety ofsoftware languages (e.g., computer code), including C, C++, Java®, Ruby,Visual Basic®, and/or other object-oriented, procedural, or otherprogramming language and development tools. Examples of computer codeinclude, but are not limited to, micro-code or micro-instructions,machine instructions, such as produced by a compiler, code used toproduce a web service, and files containing higher-level instructionsthat are executed by a computer using an interpreter. Additionalexamples of computer code include, but are not limited to, controlsignals, encrypted code, and compressed code.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example, and notlimitation. Where methods described above indicate certain eventsoccurring in certain order, the ordering of certain events can bemodified. Additionally, certain of the events may be performedconcurrently in a parallel process when possible, as well as performedsequentially as described above

1-20. (canceled)
 21. A system, comprising: a pulse waveform generatoroperatively coupled to an ablation device, the pulse waveform generatorconfigured to: select electrode sets from a plurality of electrodes ofthe ablation device, each electrode set including a first subset ofelectrodes configured to be anodes and a second subset of electrodesconfigured to be cathodes; generate voltage pulses in the form of pulsedwaveforms, each pulsed waveform including: (a) a first level of ahierarchy of the pulsed waveform that includes a first set of pulses, afirst time delay separating successive pulses of the first set ofpulses; (b) a second level of the hierarchy of the pulsed waveform thatincludes a plurality of first sets of pulses as a second set of pulses,a second time delay separating successive first sets of pulses, thesecond time delay being at least three times the duration of the firsttime delay; and (c) a third level of the hierarchy of the pulsedwaveform that includes a plurality of second sets of pulses as a thirdset of pulses, a third time delay separating successive second sets ofpulses, the third time delay being at least thirty times the duration ofthe second level time delay; and apply the voltage pulses to theelectrode sets according to a predefined sequence with at least onepulsed waveform being applied across the first and second subsets ofelectrodes of each electrode set.
 22. The system of claim 21, whereinthe pulse waveform generator is configured to apply the voltage pulsesto the electrode sets by applying the pulsed waveforms to successiveelectrode sets within the predefined sequence offset by a fourth timedelay.
 23. The system of claim 22, wherein the fourth time delay is atmost about 5 milliseconds.
 24. The system of claim 22, wherein the pulsewaveform generator is configured to generate and apply the voltagepulses such that a number of pulses in each first set of pulses, anumber of first sets of pulses in the plurality of first sets of pulsesof each second set of pulses, a number of the electrode sets within thepredefined sequence, the first time delay, the second time delay, andthe fourth time delay are jointly constrained by a Diophantineinequality.
 25. The system of claim 21, wherein the plurality ofelectrodes includes at least four electrodes, and the electrode setsinclude two electrode sets each including at least two of the at leastfour electrodes.
 26. The system of claim 21, wherein the pulse waveformgenerator is configured to apply the voltage pulses to the electrodesets during refractory periods of cardiac cycles of a heart.
 27. Thesystem of claim 21, wherein each pulse of the first set of pulses is abiphasic pulse with a voltage amplitude of at least 500 Volts and apulse time duration being in the range from about 0.5 nanosecond toabout 20 microseconds.
 28. The system of claim 21, wherein the firsttime delay is greater than a pulse time duration of each pulse of thefirst set of pulses.
 29. The system of claim 21, further comprising acardiac stimulator configured to generate pacing signals for cardiacstimulation of a heart, the pulse waveform generator further operativelycoupled to the cardiac stimulator and configured to apply the voltagepulses to the plurality of electrodes in synchrony with the pacingsignals.
 30. A system, comprising: a pulse waveform generatoroperatively coupled to an ablation device, the pulse waveform generatorconfigured to: receive a set of parameters for a pulsed waveform;generate voltage pulses in the form of pulsed waveforms according to theset of parameters, each pulsed waveform including: (a) a first level ofa hierarchy of the pulsed waveform that includes a first set of pulses,a first time delay separating successive pulses of the first set ofpulses; (b) a second level of the hierarchy of the pulsed waveform thatincludes a plurality of first sets of pulses as a second set of pulses,a second time delay separating successive first sets of pulses, thesecond time delay being at least three times the duration of the firsttime delay; and (c) a third level of the hierarchy of the pulsedwaveform that includes a plurality of second sets of pulses as a thirdset of pulses, a third time delay separating successive second sets ofpulses, the third time delay being at least thirty times the duration ofthe second level time delay; and apply the voltage pulses to an ablationdevice operatively coupled to the pulse waveform generator.
 31. Thesystem of claim 30, wherein the pulse waveform generator is configuredto apply the voltage pulses to the ablation device by applying the pulsewaveforms over a sequence of electrode sets and with a fourth time delayoffsetting application of the pulsed waveforms to successive electrodesets in the sequence.
 32. The system of claim 31, wherein the set ofparameters is a first subset of parameters, the pulse waveform generatorfurther configured to: determine a second subset of parameters for thepulsed waveform such that the first and second subsets of parameterscollectively satisfy a Diophantine inequality.
 33. The system of claim32, wherein the first and second subsets of parameters collectivelyinclude: a number of pulses in each first set of pulses, a number offirst sets of pulses in the plurality of first sets of pulses of eachsecond set of pulses, a number of electrode sets within the sequence,the first time delay, the second time delay, and the fourth time delay.34. The system of claim 33, wherein the Diophantine inequality isj[m₂(m₁w+t₁(m₁−1))+t₂(m₂−1)]+t_(d) (j−1)<T_(r), where j is the number ofelectrode sets within the sequence, m₁ is the number of pulses in eachfirst set of pulses, m₂ is the number first sets of pulses in theplurality of first set of pulses of each second set of pulses, t₁ is thefirst time delay, t₂ is the second time delay, t_(d) is the fourth timedelay, w is a pulse width of each pulse in each first set of pulses, andT_(r) is a time period of a refractory period of a cardiac cycle. 35.The system of claim 32, wherein the pulse waveform generator isconfigured to determine the second subset of parameters by: identifyinga plurality of second subsets of parameters that each with the firstsubset of parameters satisfies the Diophantine inequality; presentingthe plurality of second subsets to a user; and receiving a selectionindicative of the second subset from the plurality of second subsets tobe used to generate the voltage pulses.
 36. The system of claim 32,wherein the pulse waveform generator is configured to determine thesecond subset of parameters by: identifying a plurality of secondsubsets of parameters that each with the first subset of parameterssatisfies the Diophantine inequality; and selecting the second subsetfrom the plurality of second subsets to be used to generate the voltagepulses based on a predefined criterion.
 37. The system of claim 30,wherein each pulse of the first set of pulses is a biphasic pulse with avoltage amplitude of at least 500 Volts and a pulse time duration beingin the range from about 0.5 nanosecond to about 20 microseconds.
 38. Thesystem of claim 30, wherein the first time delay is greater than a pulsetime duration of each pulse of the first set of pulses.
 39. A method,comprising: selecting electrode sets from a plurality of electrodes ofan ablation device, each electrode set including a first subset ofelectrodes configured to be anodes and a second subset of electrodesconfigured to be cathodes; generating voltage pulses in the form ofpulsed waveforms, each pulsed waveform including: (a) a first level of ahierarchy of the pulsed waveform that includes a first set of pulses, afirst time delay separating successive pulses of the first set ofpulses; (b) a second level of the hierarchy of the pulsed waveform thatincludes a plurality of first sets of pulses as a second set of pulses,a second time delay separating successive first sets of pulses, thesecond time delay being at least three times the duration of the firsttime delay; and (c) a third level of the hierarchy of the pulsedwaveform that includes a plurality of second sets of pulses as a thirdset of pulses, a third time delay separating successive second sets ofpulses, the third time delay being at least thirty times the duration ofthe second level time delay; and applying the voltage pulses to theelectrode sets according to a predefined sequence with at least onepulsed waveform being applied across the first and second subsets ofelectrodes of each electrode set.
 40. The method of claim 39, whereinapplying the voltage pulses to the electrode sets includes applying thepulsed waveforms to successive electrode sets within the predefinedsequence offset by a fourth time delay.
 41. The method of claim 40,wherein a number of pulses in each first set of pulses, a number offirst sets of pulses in the plurality of first sets of pulses of eachsecond set of pulses, a number of the electrode sets within thepredefined sequence, the first time delay, the second time delay, andthe fourth time delay are jointly constrained by a Diophantineinequality.
 42. The method of claim 39, wherein applying the voltagepulses to the electrode sets is during refractory periods of cardiaccycles of a heart.
 43. The method of claim 39, wherein applying thevoltage pulses to the electrode sets is in synchrony with pacing signalsgenerated by a cardiac stimulator.
 44. A method, comprising: receiving aset of parameters for a pulsed waveform; generating voltage pulses inthe form of pulsed waveforms according to the set of parameters, eachpulsed waveform including: (a) a first level of a hierarchy of thepulsed waveform that includes a first set of pulses, a first time delayseparating successive pulses of the first set of pulses; (b) a secondlevel of the hierarchy of the pulsed waveform that includes a pluralityof first sets of pulses as a second set of pulses, a second time delayseparating successive first sets of pulses, the second time delay beingat least three times the duration of the first time delay; and (c) athird level of the hierarchy of the pulsed waveform that includes aplurality of second sets of pulses as a third set of pulses, a thirdtime delay separating successive second sets of pulses, the third timedelay being at least thirty times the duration of the second level timedelay; and applying the voltage pulses to an ablation device.
 45. Themethod of claim 44, wherein applying the voltage pulses to the ablationdevice includes applying the pulse waveforms over a sequence ofelectrode sets and with a fourth time delay offsetting application ofthe pulsed waveforms to successive electrode sets in the sequence. 46.The method of claim 44, wherein the set of parameters is a first subsetof parameters, the method further comprising determining a second subsetof parameters for the pulsed waveform such that the first and secondsubsets of parameters collectively satisfy a Diophantine inequality. 47.The method of claim 46, wherein the first and second subsets ofparameters collectively include: a number of pulses in each first set ofpulses, a number of first sets of pulses in the plurality of first setsof pulses of each second set of pulses, a number of electrode setswithin the sequence, the first time delay, the second time delay, andthe fourth time delay.
 48. The method of claim 47, wherein theDiophantine inequality is j[m₂(m₁w+t₁(m₁−1))+t₂(m₂−1)]+t_(d)(j−1)<T_(r),where j is the number of electrode sets within the sequence, m₁ is thenumber of pulses in each first set of pulses, m₂ is the number firstsets of pulses in the plurality of first set of pulses of each secondset of pulses, t₁ is the first time delay, t₂ is the second time delay,t_(d) is the fourth time delay, w is a pulse width of each pulse in eachfirst set of pulses, and T_(r) is a time period of a refractory periodof a cardiac cycle.
 49. The method of claim 46, wherein determining thesecond subset of parameters includes: identifying a plurality of secondsubsets of parameters that each with the first subset of parameterssatisfies the Diophantine inequality; presenting the plurality of secondsubsets to a user; and receiving a selection indicative of the secondsubset from the plurality of second subsets to be used to generate thevoltage pulses.
 50. The method of claim 46, wherein determining thesecond subset of parameters includes: identifying a plurality of secondsubsets of parameters that each with the first subset of parameterssatisfies the Diophantine inequality; and selecting the second subsetfrom the plurality of second subsets to be used to generate the voltagepulses based on a predefined criterion.